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1. What Does Low Variance Mean Absolute
2. Low Variance Vs High Variance

Normal IID samples - Unknown mean. This example is similar to the previous one. The only difference is that we now relax the assumption that the mean of the distribution is known. In this example, the sample is made of independent draws from a normal distribution having unknown mean and unknown variance.

1. . The formulas for variance listed below are for the variance of a sample. If you want to get the variance of a population, the denominator becomes 'n-1' (take the obtained value of n and subtract 1 from it). If you want to compute the standard deviation for a population, take the square root of the value obtained by calculating the variance of.
2. The variance gives an approximate idea of data volatility. 68% of values are between +1 and -1 standard deviation from the mean. That means Standard Deviation gives more details. Variance is used to know about the planned and actual behavior with a certain degree of uncertainty.
3. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.

A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another. Variance is the average of the squared distances from each point to the mean.

One problem with the variance is that it does not have the same unit of measure as the original data. For example, original data containing lengths measured in feet has a variance measured in square feet.

A low standard deviation indicates that the data points tend to be very close to the mean. A high standard deviation indicates that the data points are spread out over a large range of values.
The standard deviation can be thought of as a 'standard' way of knowing what is normal (typical), what is very large, and what is very small in the data set.

Standard deviation is a popular measure of variability because it returns to the original units of measure of the data set. For example, original data containing lengths measured in feet has a standard deviation also measured in feet.

A normal curve is a symmetric, bell-shaped curve. The center of the graph is the mean, and the height and width of the graph are determined by the standard deviation. When the standard deviation is small, the curve will be tall and narrow in spread. When the standard deviation is large, the curve will be short and wide in spread. The mean and median have the same value in a normal curve.

It is easy enough for managers to see that things in the business world vary. Some marketing campaigns produce great results; similar ones do not. There are times when the supply chain works effortlessly, and other times when every step is snarled. Some days the numbers look fine, and other days they just don’t add up. Variation is a manager’s natural enemy, making it more difficult to sort out what’s really going on, make valid predictions, and be in control.

It doesn’t have to be that way. Sorting out variation provides needed context, points to opportunity, and helps managers maintain their cool when something goes wrong. Managers should learn how to measure variation, understand what it tells them about their business, decompose it, and, when necessary, reduce it.

I advise managers to sort out variation and what is causing it. Doing so provides needed context, points to opportunity, and helps them maintain their cool when something goes wrong. Consider the following example. The figure below depicts the error rates for the first three weeks of an invoicing process:

After week two, the responsible manager was embarrassed — could her team really be performing that poorly? After the third, she breathed a sigh of relief. The error rate may be high, but at least the trend was in the right direction! She had been extolling her people to “work harder to get the error rate down.” Finally, they were listening!

Unfortunately, her interpretation did not hold up. Here are the measurements for the next seven weeks:

This manager’s illusion was shattered the very next week, as the error rate went even higher! Her mistake arose because she did not understand that all processes vary, often considerably!

This vignette underscores the first point, which is simply to acknowledge that variation is important and take it into account. Specifically, you should always ask, “What is the ‘plus/minus’ around the number?” and understand the implications. After the third week in this example, the plus/minus is fifty percent ± eight percent (42% to 58%). The “eight percent” is two standard deviations, a measure of variability explained further below. Had she taken it into account, this manager would not have been so fast to credit her exhortations to the troops with an improvement that wasn’t there. More generally, you should assume that differences within the plus/minus are due to randomness and resist the temptation to take credit or assign blame.

As you dive into the numbers, it’s important to understand the sources of variation. For instance, everyone knows that some full-grown adults are taller than others, and it is easy enough to observe that men, on average, are taller than women. So, in this instance, one component of variation is gender. Similarly, people from the Netherlands are generally taller, and those from the Philippines are generally shorter. Nationality, then, is another source of variation. It is important to understand these sources of variability if you’re in the clothing business, lest you send too many shorter pants to clothing stores in the Netherlands.

These sources become increasingly important as you gain a feel for measurements of variation. After all, you can’t manage what you don’t measure! The two most important measures of variability are called the aforementioned “standard deviation” (σ) and “R-squared (R²) Don’t be put off by the nonintuitive names. Instead, focus on interpretation.

Think of the range from one standard deviation (1σ) below the average to one standard deviation above the average as embracing about two-thirds of an overall population. Thus, as the figure below depicts, about two-thirds of full-grown U.S. women are between 5’1” and 5’7” tall. Think of the average plus/minus two standard deviations (2σ) as embracing 95% of a population, as the plot also depicts. For U.S. women, this means that only 5% are shorter than 4’10” or taller than 5’9”. Similarly, the manager responsible for the billing process should expect 95% of all measurements to fall between 42% and 58% and underscores her misinterpretation of 46% in week three.

Finally, think of the average plus/minus three standard deviations (3σ) as embracing all but a fraction of a percent of a population.

Interpret R² as the “fraction of variation due to a particular source.” The next plot features the heights of both men and women. Note that men are about five inches taller, on average, and their heights exhibit slightly higher variation. When it comes to height, clearly men and women are different. Further, the combined population of men and women varies even more. But how much variation does gender explain in this combined population? The answer is about a third. Thus, gender is an important factor, but there is much more going on. (Note: Excel, Google sheets, and good statistical and analytic packages provide the needed calculations.)

Managers should aim to identify as many important sources of variability as they can. I’ve already noted that gender and nationality are two sources. Age may well be a third, and one can identify plenty of others as well. Each has its own R² and, the larger the R², the more important the source. Once you find an important source of variation, turn your attention to creating business advantage.

Importantly, R² also applies to entire models. Thus, there is an R² for even the most complicated model for height. Again, the larger the R², the better the model.

What Does Low Variance Mean Absolute

Now let’s look back at the example with the team’s error rate. Plus/minus calculations are usually based on two standard deviations. The “eight percent” in the “fifty percent ± eight percent” above is 2σ. The responsible manager of that example should expect 95% of all measurements to fall between 42% and 58%, and underscores her misinterpretation of 46% in week three.

Understanding σ and R² enables managers to make more powerful predictions, establish control, and improve performance. The simplest predictions use 3σ limits for the plus/minus. In the next plot, I’ve added these limits (called upper and lower control limits, and labeled “ucl” and “lcl” in the plot) five weeks into the future. The manager can now safely predict that unless they take active steps to change it, the process will perform within these limits for the foreseeable future.

Low Variance Vs High Variance

To be clear, no manager should be satisfied with either this level of this performance or the associated variation and this manager was not. She and her team dug deeper, finding — then eliminating — two sources of variation. This work took several weeks, leading to the chart below.

Importantly, this manager’s job was much easier starting at week 24. Her process performed better, and three-quarters of the variation was removed, making it easier to predict a brighter future.

Understanding variation puts a powerful tool in your data science quiver. So first seek to appreciate, quantify, and identify the important sources of variation. Then reduce those you can and take the others into account to gain business advantage. Though they may not be explicit about it, all the best and most popular techniques in data science aim to help you do just that. Variation need not be your enemy. Opportunity abounds.